Decorrelation-Based Feature Discovery: Prostate-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 The Data

Prostate_DS <- read.csv("~/GitHub/LatentBiomarkers/Data/Prostate_GSE6919_U95B.csv")
colnames(Prostate_DS) <-str_replace_all(colnames(Prostate_DS),"\\.","_")
rownames(Prostate_DS) <- Prostate_DS$samples
Prostate_DS$samples <- NULL
table(Prostate_DS$type)
#> 
#>                 normal primary_prostate_tumor 
#>                     60                     64
Prostate_DS$type <- 1*(Prostate_DS$type == "primary_prostate_tumor")
table(Prostate_DS$type)
#> 
#>  0  1 
#> 60 64

1.2.0.1 Standarize the names for the reporting

studyName <- "Prostate"
dataframe <- Prostate_DS
outcome <- "type"
thro <- 0.8
cexheat = 0.10
TopVariables <- 10

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
124	12620

pander::pander(table(dataframe[,outcome]))

0	1
60	64

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  X58491_s_at X44816_s_at AFFX_BioB_M_at X54789_at X43849_s_at X52300_f_at 
#> X41880_at X41881_at X41882_at X41883_at X41884_at X41885_at 
#> 0.7446117 0.4186212 0.2634707 0.3645800 0.6194929 0.1778922 
#> 
#>  Included: 12620 , Uni p: 1.18859e-05 , Base Size: 37 , Rcrit: 0.3697266 
#> 
#> 
 1 <R=0.988,thr=0.950>, Top: 24< 1 >[Fa= 24 ]( 24 , 27 , 0 ),<|><>Tot Used: 51 , Added: 27 , Zero Std: 0 , Max Cor: 0.949
#> 
 2 <R=0.949,thr=0.900>, Top: 40< 1 >[Fa= 59 ]( 40 , 45 , 24 ),<|><>Tot Used: 130 , Added: 45 , Zero Std: 0 , Max Cor: 0.915
#> 
 3 <R=0.915,thr=0.900>, Top: 2< 1 >[Fa= 61 ]( 2 , 2 , 59 ),<|><>Tot Used: 134 , Added: 2 , Zero Std: 0 , Max Cor: 0.908
#> 
 4 <R=0.908,thr=0.900>, Top: 1< 1 >[Fa= 62 ]( 1 , 1 , 61 ),<|><>Tot Used: 136 , Added: 1 , Zero Std: 0 , Max Cor: 0.899
#> 
 5 <R=0.899,thr=0.800>, Top: 135< 1 >.[Fa= 186 ]( 134 , 208 , 62 ),<|><>Tot Used: 460 , Added: 208 , Zero Std: 0 , Max Cor: 0.890
#> 
 6 <R=0.890,thr=0.800>, Top: 23< 2 >[Fa= 207 ]( 21 , 28 , 186 ),<|><>Tot Used: 509 , Added: 28 , Zero Std: 0 , Max Cor: 0.816
#> 
 7 <R=0.816,thr=0.800>, Top: 2< 1 >[Fa= 209 ]( 2 , 2 , 207 ),<|><>Tot Used: 513 , Added: 2 , Zero Std: 0 , Max Cor: 0.800
#> 
 8 <R=0.800,thr=0.800>
#> 
 [ 8 ], 0.7988513 Decor Dimension: 513 Nused: 513 . Cor to Base: 300 , ABase: 12620 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

783

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

719

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.71

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

4.29

varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))

La_AFFX_BioC_3_at	La_X44840_s_at	La_AFFX_BioB_5_at	La_X47004_at	La_AFFX_BioB_3_at	La_X43818_at
0.038	0.0368	0.027	0.0239	0.0238	0.023

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 513

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 102

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

[1] 102

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
      fc <- cluster_optimal(gr)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }

pander::pander(clustable)

	Formula	Class	ResidualVariance	Fscore
X48039_at	NA	1	1.000	40
X43355_s_at	+ X43355_s_at - (0.470)X48039_at	1	0.285	-1
X43395_s_at	+ X43395_s_at - (0.273)X48039_at	1	0.344	-1
X43817_f_at	+ X43817_f_at - (0.618)X48039_at	1	0.294	-1
X44088_at	+ X44088_at - (0.449)X48039_at	1	0.256	-1
X44119_at	+ X44119_at - (0.413)X48039_at	1	0.283	-1
X44746_at	+ X44746_at - (0.219)X48039_at	1	0.355	-1
X45178_at	+ X45178_at - (0.218)X48039_at	1	0.359	-1
X45199_at	+ X45199_at - (0.535)X48039_at	1	0.345	-1
X45680_at	+ X45680_at - (0.327)X48039_at	1	0.281	-1
X45777_at	+ X45777_at - (0.367)X48039_at	1	0.300	-1
X46276_at	+ X46276_at - (0.879)X48039_at	1	0.234	-1
X46314_at	+ X46314_at - (0.450)X48039_at	1	0.300	-1
X46476_at	+ X46476_at - (0.655)X48039_at	1	0.239	-1
X48927_at	- (0.383)X48039_at + X48927_at	1	0.332	-1
X50001_at	- (0.519)X48039_at + X50001_at	1	0.262	-1
X50361_at	- (0.929)X48039_at + X50361_at	1	0.077	-1
X51939_at	- (1.007)X48039_at + X51939_at	1	0.151	-1
X52036_at	- (0.293)X48039_at + X52036_at	1	0.316	-1
X52140_at	- (0.756)X48039_at + X52140_at	1	0.164	-1
X52856_at	- (0.322)X48039_at + X52856_at	1	0.303	-1
X52946_at	- (0.518)X48039_at + X52946_at	1	0.251	-1
X53785_at	- (0.383)X48039_at + X53785_at	1	0.265	-1
X53796_at	- (0.617)X48039_at + X53796_at	1	0.288	-1
X54063_at	- (0.514)X48039_at + X54063_at	1	0.233	-1
X54668_at	- (0.628)X48039_at + X54668_at	1	0.308	-1
X54713_at	- (0.474)X48039_at + X54713_at	1	0.262	-1
X54992_at	- (0.345)X48039_at + X54992_at	1	0.302	-1
X55077_at	- (0.356)X48039_at + X55077_at	1	0.308	-1
X56192_at	- (0.501)X48039_at + X56192_at	1	0.348	-1
X56474_at	- (0.586)X48039_at + X56474_at	1	0.234	-1
X57194_at	- (0.380)X48039_at + X57194_at	1	0.249	-1
X57709_at	- (0.205)X48039_at + X57709_at	1	0.314	-1
X58917_at	- (0.179)X48039_at + X58917_at	1	0.338	-1
X47281_r_at	NA	2	1.000	7
X44476_r_at	+ X44476_r_at - (0.781)X47281_r_at	2	0.340	-1
X45020_r_at	+ X45020_r_at - (0.533)X47281_r_at	2	0.316	-1
X46940_r_at	+ X46940_r_at - (0.527)X47281_r_at	2	0.357	-1
X47428_r_at	- (0.514)X47281_r_at + X47428_r_at	2	0.344	-1
X47708_r_at	- (0.663)X47281_r_at + X47708_r_at	2	0.246	-1
X48326_r_at	- (0.584)X47281_r_at + X48326_r_at	2	0.337	-1
X54192_r_at	- (0.600)X47281_r_at + X54192_r_at	2	0.270	-1
X44986_s_at	NA	3	1.000	6
X44841_at	+ X44841_at - (0.888)X44986_s_at	3	0.110	-1
X45628_at	- (0.728)X44986_s_at + X45628_at	3	0.337	-1
X46698_at	- (0.907)X44986_s_at + X46698_at	3	0.336	-1
X53793_at	- (1.184)X44986_s_at + X53793_at	3	0.286	-1
X54865_at	- (1.250)X44986_s_at + X54865_at	3	0.359	-1
X55722_at	- (1.070)X44986_s_at + X55722_at	3	0.310	-1
X47112_at	NA	4	1.000	6

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data

  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

X56456_at, X52119_at, X45793_at, X46410_at, X54033_at and X54063_at

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

X56456_at, X52119_at, X45793_at, X46410_at, X54033_at and X56471_at

  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : X41979_r_at 200 : X42079_at 300 : X42179_at 400 : X42279_at 500 : X42379_at
600 : X42479_r_at 700 : X42579_at 800 : X42679_at 900 : X42779_at 1000 : X42879_at
1100 : X42979_at 1200 : X43079_at 1300 : X43179_at 1400 : X43279_at 1500 : X43379_f_at
1600 : X43479_at 1700 : X43579_at 1800 : X43679_at 1900 : X43779_at 2000 : X43879_at
2100 : X43979_r_at 2200 : X44079_at 2300 : X44179_at 2400 : X44279_at 2500 : X44379_at
2600 : X44479_at 2700 : X44579_at 2800 : X44679_at 2900 : X44779_at 3000 : X44879_at
3100 : X44979_at 3200 : X45079_at 3300 : X45179_at 3400 : X45279_at 3500 : X45379_at
3600 : X45479_at 3700 : X45579_at 3800 : X45679_at 3900 : X45779_at 4000 : X45879_at
4100 : X45979_at 4200 : X46079_at 4300 : X46179_f_at 4400 : X46279_at 4500 : X46379_i_at
4600 : X46479_at 4700 : X46579_at 4800 : X46679_at 4900 : X46779_r_at 5000 : X46879_at
5100 : X46979_at 5200 : X47079_at 5300 : X47179_r_at 5400 : X47279_r_at 5500 : X47379_at
5600 : X47479_at 5700 : X47579_at 5800 : X47679_at 5900 : X47779_at 6000 : X47879_at
6100 : X47979_at 6200 : X48079_at 6300 : X48179_at 6400 : X48279_at 6500 : X48379_at
6600 : X48479_at 6700 : X48579_r_at 6800 : X48790_s_at 6900 : X48981_at 7000 : X49161_at
7100 : X49345_at 7200 : X49549_at 7300 : X49727_at 7400 : X49908_at 7500 : X50100_at
7600 : X50266_at 7700 : X50463_at 7800 : X50660_r_at 7900 : X50860_at 8000 : X51020_at
8100 : X51179_at 8200 : X51365_at 8300 : X51567_at 8400 : X51747_at 8500 : X51927_at
8600 : X52116_at 8700 : X52327_s_at 8800 : X52550_s_at 8900 : X52760_at 9000 : X52958_at
9100 : X53176_at 9200 : X53374_at 9300 : X53575_at 9400 : X53781_at 9500 : X53965_at
9600 : X54171_s_at 9700 : X54367_at 9800 : X54557_at 9900 : X54755_at 10000 : X54962_f_at
10100 : X55157_at 10200 : X55359_at 10300 : X55532_at 10400 : X55709_at 10500 : X55902_at
10600 : X56086_at 10700 : X56263_at 10800 : X56441_at 10900 : X56637_at 11000 : X56832_at
11100 : X57023_at 11200 : X57205_at 11300 : X57382_at 11400 : X57590_at 11500 : X57797_at
11600 : X57996_at 11700 : X58195_at 11800 : X58394_g_at 11900 : X58617_at 12000 : X58812_at
12100 : X58984_at 12200 : X59194_at 12300 : X59378_at 12400 : X59555_at 12500 : X59729_at
12600 : AFFX_LysX_M_at

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : X41979_r_at 200 : X42079_at 300 : X42179_at 400 : X42279_at 500 : X42379_at
600 : X42479_r_at 700 : X42579_at 800 : X42679_at 900 : X42779_at 1000 : X42879_at
1100 : X42979_at 1200 : X43079_at 1300 : X43179_at 1400 : X43279_at 1500 : X43379_f_at
1600 : X43479_at 1700 : X43579_at 1800 : X43679_at 1900 : X43779_at 2000 : X43879_at
2100 : X43979_r_at 2200 : X44079_at 2300 : X44179_at 2400 : X44279_at 2500 : X44379_at
2600 : X44479_at 2700 : X44579_at 2800 : X44679_at 2900 : X44779_at 3000 : X44879_at
3100 : X44979_at 3200 : X45079_at 3300 : X45179_at 3400 : X45279_at 3500 : X45379_at
3600 : X45479_at 3700 : La_X45579_at 3800 : X45679_at 3900 : X45779_at 4000 : X45879_at
4100 : X45979_at 4200 : X46079_at 4300 : La_X46179_f_at 4400 : X46279_at 4500 : X46379_i_at
4600 : X46479_at 4700 : X46579_at 4800 : X46679_at 4900 : X46779_r_at 5000 : X46879_at
5100 : X46979_at 5200 : X47079_at 5300 : X47179_r_at 5400 : X47279_r_at 5500 : X47379_at
5600 : X47479_at 5700 : X47579_at 5800 : X47679_at 5900 : X47779_at 6000 : X47879_at
6100 : X47979_at 6200 : X48079_at 6300 : X48179_at 6400 : X48279_at 6500 : X48379_at
6600 : X48479_at 6700 : X48579_r_at 6800 : X48790_s_at 6900 : X48981_at 7000 : X49161_at
7100 : X49345_at 7200 : X49549_at 7300 : X49727_at 7400 : X49908_at 7500 : X50100_at
7600 : X50266_at 7700 : X50463_at 7800 : X50660_r_at 7900 : X50860_at 8000 : X51020_at
8100 : X51179_at 8200 : X51365_at 8300 : X51567_at 8400 : X51747_at 8500 : X51927_at
8600 : X52116_at 8700 : X52327_s_at 8800 : X52550_s_at 8900 : X52760_at 9000 : X52958_at
9100 : X53176_at 9200 : X53374_at 9300 : X53575_at 9400 : X53781_at 9500 : X53965_at
9600 : X54171_s_at 9700 : X54367_at 9800 : X54557_at 9900 : X54755_at 10000 : X54962_f_at
10100 : X55157_at 10200 : X55359_at 10300 : X55532_at 10400 : X55709_at 10500 : X55902_at
10600 : X56086_at 10700 : X56263_at 10800 : X56441_at 10900 : X56637_at 11000 : X56832_at
11100 : X57023_at 11200 : X57205_at 11300 : X57382_at 11400 : X57590_at 11500 : X57797_at
11600 : X57996_at 11700 : X58195_at 11800 : X58394_g_at 11900 : X58617_at 12000 : X58812_at
12100 : X58984_at 12200 : X59194_at 12300 : X59378_at 12400 : X59555_at 12500 : X59729_at
12600 : AFFX_LysX_M_at

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
X56456_at	5.76	0.515	6.36	0.494	0.999	0.804
X46410_at	3.57	0.370	4.03	0.492	0.281	0.796
X45793_at	5.61	0.396	6.03	0.344	0.989	0.794
X54865_at	3.64	0.513	4.26	0.559	0.521	0.792
X51726_at	3.51	0.213	3.74	0.240	0.485	0.783
X50361_at	7.74	1.289	8.93	0.874	0.505	0.781
X56474_at	6.22	0.760	7.06	0.769	0.858	0.780
X54063_at	4.63	0.711	5.36	0.629	0.999	0.780
X45178_at	4.30	0.299	4.64	0.326	0.988	0.779
X43355_s_at	6.02	0.652	6.69	0.623	0.466	0.779

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
X56456_at	5.763	0.5154	6.361	0.4938	0.9988	0.804
X46410_at	3.566	0.3704	4.026	0.4919	0.2809	0.796
X45793_at	5.608	0.3965	6.028	0.3445	0.9888	0.794
X51726_at	3.505	0.2133	3.735	0.2397	0.4849	0.783
X45156_at	6.554	0.3967	6.940	0.3186	0.9029	0.779
X45674_at	3.080	0.3720	3.452	0.3399	0.9674	0.778
X45340_at	4.557	0.4729	4.997	0.4290	0.8732	0.778
X52119_at	6.167	0.4012	5.811	0.3591	0.0399	0.771
X53011_at	4.530	0.4330	4.932	0.3688	0.7642	0.770
X48506_at	5.243	0.3233	5.551	0.2887	0.3136	0.769
La_X46715_at	0.257	0.2128	0.373	0.1826	0.6400	0.676
La_X54865_at	-3.644	0.3127	-3.422	0.3935	0.6602	0.664
La_X46287_at	3.222	0.2326	3.335	0.1992	0.4845	0.661
La_X45802_at	1.976	0.0713	2.023	0.0804	0.9086	0.660
La_X48760_s_at	-0.776	0.1906	-0.676	0.1474	0.4877	0.656

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2	313	0.0248

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores	varratio
X56456_at	NA	5.763	0.5154	6.361	0.4938	0.9988	0.804	0.804	0	1.000
X46410_at	NA	3.566	0.3704	4.026	0.4919	0.2809	0.796	0.796	0	1.000
X45793_at	NA	5.608	0.3965	6.028	0.3445	0.9888	0.794	0.794	1	1.000
X54865_at	NA	3.643	0.5133	4.259	0.5589	0.5215	0.792	0.792	NA	NA
X51726_at	NA	3.505	0.2133	3.735	0.2397	0.4849	0.783	0.783	0	1.000
X50361_at	NA	7.736	1.2892	8.927	0.8741	0.5051	0.781	0.781	NA	NA
X56474_at	NA	6.220	0.7597	7.057	0.7690	0.8581	0.780	0.780	NA	NA
X54063_at	NA	4.632	0.7106	5.357	0.6288	0.9989	0.780	0.780	NA	NA
X45178_at	NA	4.303	0.2994	4.638	0.3256	0.9885	0.779	0.779	NA	NA
X43355_s_at	NA	6.016	0.6523	6.694	0.6229	0.4656	0.779	0.779	NA	NA
X45156_at	NA	6.554	0.3967	6.940	0.3186	0.9029	0.779	0.779	0	1.000
X45674_at	NA	3.080	0.3720	3.452	0.3399	0.9674	0.778	0.778	0	1.000
X45340_at	NA	4.557	0.4729	4.997	0.4290	0.8732	0.778	0.778	1	1.000
X52119_at	NA	6.167	0.4012	5.811	0.3591	0.0399	0.771	0.771	0	1.000
X53011_at	NA	4.530	0.4330	4.932	0.3688	0.7642	0.770	0.770	0	1.000
X48506_at	NA	5.243	0.3233	5.551	0.2887	0.3136	0.769	0.769	0	1.000
La_X46715_at	+ X46715_at - (0.765)X46739_at	0.257	0.2128	0.373	0.1826	0.6400	0.676	0.689	-1	0.321
La_X54865_at	- (1.250)X44986_s_at + X54865_at	-3.644	0.3127	-3.422	0.3935	0.6602	0.664	0.792	-1	0.359
La_X46287_at	+ X46287_at - (0.478)X52333_f_at	3.222	0.2326	3.335	0.1992	0.4845	0.661	0.726	-1	0.320
La_X45802_at	- (0.754)X44787_s_at + X45802_at	1.976	0.0713	2.023	0.0804	0.9086	0.660	0.649	-1	0.249
La_X48760_s_at	- (1.182)X45500_at + X48760_s_at	-0.776	0.1906	-0.676	0.1474	0.4877	0.656	0.582	-1	0.163

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	57	3
1	11	53

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.887	0.818	0.937
3	se	0.828	0.713	0.911
4	sp	0.950	0.861	0.990
6	diag.or	91.545	24.205	346.226

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	57	3
1	11	53

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.887	0.818	0.937
3	se	0.828	0.713	0.911
4	sp	0.950	0.861	0.990
6	diag.or	91.545	24.205	346.226

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	46	14
1	7	57

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.831	0.753	0.892
3	se	0.891	0.788	0.955
4	sp	0.767	0.640	0.866
6	diag.or	26.755	9.972	71.785

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	57	3
1	11	53

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.887	0.818	0.937
3	se	0.828	0.713	0.911
4	sp	0.950	0.861	0.990
6	diag.or	91.545	24.205	346.226

  par(op)